As Andy Barker — an accountant-turned-detective — Andy Richter fights crime while outfitted in short-sleeve dress shirts, his briefcase full of Dilbert cartoons, his baby-sunshine face set in a determined grin. If that were the only gag, the show would still be fairly funny. (Conan O’Brien’s old sidekick won boundless comedic goodwill with Fox’s short-lived Andy Richter Controls the Universe — enough even to see him through Fox’s short-lived Quintuplets.) But the NBC comedy has more to offer than squareguy jokes. Andy Barker, P.I. has the aesthetics of a great old ’70s detective show — all wood paneling and wakaja-wakaja. And the comedy, co-created by O’Brien, pays tribute to the Zuckers’ Police Squad! series: There’s a scene in which Andy’s face is suddenly engulfed by an attacking chicken — you can almost see Leslie Nielsen’s sport coat flapping behind the feathers.

This updated detective satire plops Andy’s office not on some shady downtown drag, but in a sprawling, sun-scorched California strip mall, where he’s quickly befriended by fellow tenant Simon (Arrested Development’s Tony Hale, still twitchy as a greedy bunny). Simon manages a video store, which, unfortunately, leads to strings of movie references from Chinatownto The Godfather to Jungle Fever to Miss Congeniality 2. (Overpacked, obscure pop culture riffs are like pirate jokes — very mid-aughts and hopefully on the decline.) But Andy Barker quickly eases back from these easy targets and gets wonderfully loose. The show isn’t afraid to be quiet, taking its cue from its mild-mannered title character, who utters no oaths stronger than ”Mother Hubbard!” In one episode, a venal, steamboat-size slob is murdered, and the funniest bits aren’t the guy’s passionate eating binges (”The man kept a thermos of emergency bisque!” marvels Andy), but the reaction shots of Andy politely trying to hide his shock at hearing the deceased’s many lovers lust over him. ”You thiiiink?” he squints when the guy’s wife suggests he had a mistress. Richter’s inherent archness is nicely anchored by septuagenarian Harve Presnell, a character actor best known as William H. Macy’s badass father-in-law in Fargo. Presnell plays Andy’s equally badass detective mentor, and it’s a sign of the show’s underdog ethos that the leatherjacketed AARP member is the resident stud here.

Andy Barker isn’t as complete a comedy as Andy Richter Controls the Universe — the first three episodes feel like a series of very funny bits that have been welded together. But so did 30 Rock when it first started, and that’s now the best comedy on TV. Let’s hope NBC gives Barker time to find its groove. Although when an entire episode is based around a ”murderous chicken cartel,” there’s not too much room for improvement.